Question

Sales of Body           Price of Lens             Gender           Sales of Lens

                        155                 $700                             1                             122

                        101                     650                             1                             120

                        157                     725                            0                             135

                        180                     575                             1                             95

                        150                     600                             0                             100

                        201                     750                             0                             174

                        99                     560                             1                             118

                        137                    500                             0                             130

                        155                             675                             1                                  128

                        165                             550                             1                                  166

                        152                            725                             0                                  131

                        127                             750                             1                                  102

                        217                             565                             0                                  165

                        186                             670                             0                                  154

                        176                             600                             1                                  97

                        123                             585                             0                                  129

                        109                             645                             0                                  98

                        90                             575                             1                                  105

                        176                             660                             0                                  120

                        129                             650                             1                                  105

a)         Find the regression coefficients and the regression equation for this data by using the method of least squares analysis.

b)         Provide meanings for each of the regression coefficients. Be sure these meanings relate specifically to the context of the problem.

c)          Use your regression equation to predict the sales of the lens when sales of the camera body are 200 and the price of the lens is $800. Do the same when the sales of the camera body are 150 and the price of the lens is $700. Do you have any concerns with either of these predictions? State a reason or reasons for any concerns you might have.

Answer 1

Using Minitab:

a)

Regression Analysis: Sales of Lens versus Sales of Body, Price of Lens The regression equation is Sales of Lens = 66.39 + 0.3821 Sales of Body + 0.0020 Price of Lens Predictor Coef SE Coef Constant 66.39 46.03 Sales of Body 0.3821 0.1424 Price of Lens | 0.0020 0.06878 т 1.44 2.68 0.03 P 0.167 0.016 0.977 S = 21.4172 R-Sq = 30.3% R-Sq(adj) = 22.1%

b) Coefficient of Sales of Body: When a unit increase on the Sales of Body, the mean Sales of the Lens increase by 0.3821 unit at fixe Price of Lens variable.

Coefficient of Price of Lens: When a unit increase on the Price of Lens, the mean Sales of the Lens increase by 0.0.0020 unit at fixe Sales of Body variable.

Coefficient of Intercept: When both Sales of Body and Price of Lens variables are zero, the mean Sales of the Lens is 66.39.

c) The predicted sales of the lens when sales of the camera body are 200 and the price of the lens is $800 is

Sales of Lens = 66.39 + 0.3821*200 + 0.0020*800=144.41.

The predicted sales of the lens when sales of the camera body are 150 and the price of the lens is $700 is

Sales of Lens = 66.39 + 0.3821*150 + 0.0020*700=125.105

Discussion: The price of the lens $800 is a vlaue which comes from the minimum and maximum value of the give data of the variable price of the lens. Hence, the variance of the predicted value of Sales of Lens will have larger when camera body=200 and price of the lens=$800 compare with the variance of the predicted value of Sales of Lens will have larger when camera body=150 and price of the lens=$700.